V-drome has accurately identified your
lamp:
Egyptian 'frog
lamp', 2nd to 3rd or 4th centuries AD. (The slightly later dates given for the example in the
Budapest museum are based on early speculation and do not agree with modern research.)
I will just add that the mark on the base - the Greek letter
alpha (upside-down in your first image of it) - is extremely common on this
type of
lamp. Its ubiquity suggests that it is generic rather than being restricted to a specific maker or workshop but its significance is currently unknown - perhaps it held a religious or cultic meaning.
I suspect your
lamp is probably authentic. The colour of the clay for these
lamps varied from pale buff to dark red-brown or grey. The glossy surface may well be the result of a relatively modern varnish or wax - a common treatment for artefacts in Victorian times,
applied in the misinformed belief that it made them more attractive and helped to preserve them.
There are one or two examples of the general
type included on my website:
http://www.romulus2.com/lamps/lampcat/lampcat3.shtml#egypt